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Multioctave supercontinuum generation and frequency conversion based on rotational nonlinearity

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Science Advances  21 Aug 2020:
Vol. 6, no. 34, eabb5375
DOI: 10.1126/sciadv.abb5375
  • Fig. 1 Nonlinear indices and phase shifts.

    The nonlinear indices of refraction of Ar, N2, and N2O (A to C) are calculated for short (30 fs) and long (280 fs) input pulse durations. Ar and N2 share similar ionization potentials and instantaneous nonlinear refractive indices. Both atomic and molecular systems exhibit an instantaneous response Δni due to the electronic Kerr nonlinearity, while the delayed rotational response Δnd, proportional to the degree of alignment in the molecular ensemble, is present only in the molecular systems. For short input pulses, the effective change in refractive index is approximately the same in Ar and N2 because only the instantaneous contribution takes effect during the period of interaction, whereas the long pulses see a significantly larger Δn in N2. The effect is even more pronounced in N2O, which was chosen because of its larger polarizability anisotropy and longer rotational period. The latter plays a crucial role because the degree to which the temporal evolution of the refractive index coincides with the intensity envelope (shown in gray for the 280-fs pulse) determines the shape of temporal phase shift and thus the time dependence of the instantaneous frequency (D).

  • Fig. 2 Pulse duration dependence of spectral broadening.

    Comparison of the supercontinuum spectra simulated in (A) Ar (6.5 bar), (B) N2 (6.5 bar), and (C) N2O (4.4 bar) for different input pulse durations at a fixed intensity of 1 TW/cm2 reveals the dynamics associated with ∆nd. In the molecular gases, longer pulses lead to larger degrees of molecular alignment and therefore enhanced nonlinearity. At the same time, the molecular alignment is delayed with respect to the pulse. The combination of these two effects leads to purely red-shifted supercontinuum spectra for pulse durations of approximately 100 fs in N2 and 150 fs in N2O. Further increasing the pulse duration shifts the peak of the alignment to coincide with the trailing edge of the pulse, resulting in more symmetric spectra and optimized spectral bandwidth for pulse durations of approximately 150 fs in N2 and 280 fs in N2O. The central frequency of the input laser was 0.29 fs−1 in all cases.

  • Fig. 3 Supercontinuum spectra.

    Supercontinuum spectra measured at the output of the fiber (A to C) show qualitative differences for atomic and molecular gases. Despite similar contributions from electronic Kerr nonlinearity, the spectrum from N2 is 2.4 times broader than that of Ar. Moreover, both the N2 and N2O spectra display strong well-spaced interference modulations in the longest wavelength components, while the shortest wavelengths are comparatively smooth. This behavior is consistent with the delayed peak of the time-dependent nonlinear refractive index, which occurs on the trailing edge of the pulse as shown in Fig. 1. We additionally find qualitative agreement with spectra obtained from numerical propagation simulations (D to F) incorporating both the instantaneous and delayed response of the refractive index.

  • Fig. 4 Pulse compression.

    Retrieved temporal (A to C) and spectral intensity (D to F) profiles of few-cycle pulses obtained for the three compression demonstrations: 6.5 bar of N2 using dispersive mirrors (A and D), 2.4 bar of N2O using dispersive mirrors (B and E), and 3.0 bar of N2O using a programmable dispersive filter (C and F). The retrieved temporal intensity profiles (red) are normalized relative to the peak intensity of the bandwidth-limited pulse profiles (blue) calculated from the retrieved spectra. The retrieved (red) and measured (gray) spectral intensity profiles are shown along with the retrieved spectral phase (blue). In all cases, the pulses are compressed close to their bandwidth-limited durations despite the presence of residual high-order dispersion.

Supplementary Materials

  • Supplementary Materials

    Multioctave supercontinuum generation and frequency conversion based on rotational nonlinearity

    John E. Beetar, M. Nrisimhamurty, Tran-Chau Truong, Garima C. Nagar, Yangyang Liu, Jonathan Nesper, Omar Suarez, Federico Rivas, Yi Wu, Bonggu Shim, Michael Chini

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    • Supplementary Methods
    • Figs. S1 to S10
    • Table S1
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